That is a good point. There are some reasons to argue otherwise (such as the shorter lifespan of animals, non monogamous behavior in the animal kingdom, etc.), but such reasons could not easily account for the obvious genetic diversity that we actually see. More likely, the origin of the Flood myth was regional, and the animals saved were merely domesticated animals.
Geneticists point to a genetic bottleneck in the human species about 70,000 years ago
For the mitochondrial eve, the numbers are much earlier than that (170,000 years), but that genetic bottleneck wouldn't seem relevant to the flood myth.
which reduced the population to less than 2,000 breeding individuals. Biblical literalists would have you believe the human race was reduced to eight individuals less than 6,000 years ago. The genes don't bear that out.
Those two points really shouldn't be mixed. The "6,000 years ago" folly is reliably discounted. But the "reduced to eight individuals" cannot be discounted quite so easily. The scenarios usually presented account for the single ancestor by means of conjecture rather than by any deterministic resolution.
In addition, every species but the "clean" species were supposedly reduced to two breeding individuals less than 6,000 years ago (the clean animals got lucky with 14 breeding individuals each). If this were the case just about every other animal on Earth would evince less genetic diversity than humanity. The evidence does not bear this out. Indeed, I can think of only two animals in worse shape genetically than humanity -- dingos and cheatahs
This is probably the second best evidence against the traditional belief of a universal flood (the best being, "where did all that water go that was covering the whole earth?").
There is no version of the universal flood that can be squared with scientific biology and geology. If folks want to believe in a miracle they should not be attempting to rationalize it.